Archive for astrostatistics

a book and two chapters on mixtures

Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , on January 8, 2019 by xi'an

The Handbook of Mixture Analysis is now out! After a few years of planning, contacts, meetings, discussions about notations, interactions with authors, further interactions with late authors, repeating editing towards homogenisation, and a final professional edit last summer, this collection of nineteen chapters involved thirty-five contributors. I am grateful to all participants to this piece of work, especially to Sylvia Früwirth-Schnatter for being a driving force in the project and for achieving a much higher degree of homogeneity in the book than I expected. I would also like to thank Rob Calver and Lara Spieker of CRC Press for their boundless patience through the many missed deadlines and their overall support.

Two chapters which I co-authored are now available as arXived documents:

5. Gilles Celeux, Kaniav Kamary, Gertraud Malsiner-Walli, Jean-Michel Marin, and Christian P. Robert, Computational Solutions for Bayesian Inference in Mixture Models
7. Gilles Celeux, Sylvia Früwirth-Schnatter, and Christian P. Robert, Model Selection for Mixture Models – Perspectives and Strategies

along other chapters

1. Peter Green, Introduction to Finite Mixtures
8. Bettina Grün, Model-based Clustering
12. Isobel Claire Gormley and Sylvia Früwirth-Schnatter, Mixtures of Experts Models
13. Sylvia Kaufmann, Hidden Markov Models in Time Series, with Applications in Economics
14. Elisabeth Gassiat, Mixtures of Nonparametric Components and Hidden Markov Models
19. Michael A. Kuhn and Eric D. Feigelson, Applications in Astronomy

improperties on an astronomical scale

Posted in Books, pictures, Statistics with tags , , , , , , , on December 15, 2017 by xi'an

As pointed out by Peter Coles on his blog, In the Dark, Hyungsuk Tak, Sujit Ghosh, and Justin Ellis just arXived a review of the unsafe use of improper priors in astronomy papers, 24 out of 75 having failed to establish that the corresponding posteriors are well-defined. And they exhibit such an instance (of impropriety) in a MNRAS paper by Pihajoki (2017), which is a complexification of Gelfand et al. (1990), also used by Jim Hobert in his thesis. (Even though the formal argument used to show the impropriety of the posterior in Pihajoki’s paper does not sound right since it considers divergence at a single value of a parameter β.) Besides repeating this warning about an issue that was rather quickly identified in the infancy of MCMC, if not in the very first publications on the Gibbs sampler, the paper seems to argue against using improper priors due to this potential danger, stating that instead proper priors that include all likely values and beyond are to be preferred. Which reminds me of the BUGS feature of using a N(0,10⁹) prior instead of the flat prior, missing the fact that “very large” variances do impact the resulting inference (if only for the issue of model comparison, remember Lindley-Jeffreys!). And are informative in that sense. However, it is obviously a good idea to advise checking for propriety (!) and using such alternatives may come as a safety button, providing a comparison benchmark to spot possible divergences in the resulting inference.

[Astrostat summer school] fogrise [jatp]

Posted in Kids, Mountains, pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , on October 11, 2017 by xi'an

[Astrostat summer school] sunrise [jatp]

Posted in Statistics with tags , , , , , , , , , , , on October 10, 2017 by xi'an

[summer Astrostat school] room with a view [jatp]

Posted in Mountains, pictures, R, Running, Statistics, Travel, University life with tags , , , , , , , , , , on October 9, 2017 by xi'an

I just arrived in Autrans, on the Plateau du Vercors overlooking Grenoble and the view is fabulistic! Trees have started to turn red and yellow, the weather is very mild, and my duties are restricted to teaching ABC to a group of enthusiastic astronomers and cosmologists..! Second advanced course on ABC in the mountains this year, hard to beat (except by a third course). The surroundings are so serene and peaceful that I even conceded to install RStudio for my course! Instead of sticking to my favourite vim editor and line commands.

Bayesian methods in cosmology

Posted in Statistics with tags , , , , , , , , , , , , on January 18, 2017 by xi'an

A rather massive document was arXived a few days ago by Roberto Trotta on Bayesian methods for cosmology, in conjunction with an earlier winter school, the 44th Saas Fee Advanced Course on Astronomy and Astrophysics, “Cosmology with wide-field surveys”. While I never had the opportunity to give a winter school in Saas Fee, I will give next month a course on ABC to statistics graduates in another Swiss dream location, Les Diablerets.  And next Fall a course on ABC again but to astronomers and cosmologists, in Autrans, near Grenoble.

The course document is an 80 pages introduction to probability and statistics, in particular Bayesian inference and Bayesian model choice. Including exercises and references. As such, it is rather standard in that the material could be found as well in textbooks. Statistics textbooks.

When introducing the Bayesian perspective, Roberto Trotta advances several arguments in favour of this approach. The first one is that it is generally easier to follow a Bayesian approach when compared with seeking a non-Bayesian one, while recovering long-term properties. (Although there are inconsistent Bayesian settings.) The second one is that a Bayesian modelling allows to handle naturally nuisance parameters, because there are essentially no nuisance parameters. (Even though preventing small world modelling may lead to difficulties as in the Robbins-Wasserman paradox.) The following two reasons are the incorporation of prior information and the appeal on conditioning on the actual data.

trottaThe document also includes this above and nice illustration of the concentration of measure as the dimension of the parameter increases. (Although one should not over-interpret it. The concentration does not occur in the same way for a normal distribution for instance.) It further spends quite some space on the Bayes factor, its scaling as a natural Occam’s razor,  and the comparison with p-values, before (unsurprisingly) introducing nested sampling. And the Savage-Dickey ratio. The conclusion of this model choice section proposes some open problems, with a rather unorthodox—in the Bayesian sense—line on the justification of priors and the notion of a “correct” prior (yeech!), plus an musing about adopting a loss function, with which I quite agree.

Bayesian astrostats under Laplace’s gaze

Posted in Books, Kids, pictures, Statistics, Travel, University life, Wines with tags , , , , , , , , , , , on October 11, 2016 by xi'an

This afternoon, I was part of a jury of an astrostatistics thesis, where the astronomy part was about binary objects in the Solar System, and the statistics part about detecting patterns in those objects, unsurprisingly. The first part was highly classical using several non-parametric tests like Kolmogorov-Smirnov to test whether those binary objects were different from single objects. While the p-values were very tiny, I felt these values were over-interpreted in the thesis, because the sample size of N=30 leads to some scepticism about numerical quantities like 0.0008. While I do not want to sound pushing for Bayesian solutions in every setting, this case is a good illustration of the nefarious power of p-values, which are almost always taken at face value, i.e., where 0.008 is understood in terms of the null hypothesis and not in terms of the observed realisation of the p-value. Even within a frequentist framework, the distribution of this p-value should be evaluated or estimated one way or another, as there is no reason to believe it is anywhere near a Uniform(0,1) distribution.The second part of the thesis was about the estimation of some parameters of the laws of the orbits of those dual objects and the point of interest for me was the purely mechanical construction of a likelihood function that was an exponential transform of a sum of residuals, made of squared differences between the observations and their expectations. Or a power of such differences. This was called the “statistical model” in the thesis and I presume in part of the astrostats literature. This reminded me of the first meeting I had with my colleagues from Besançon, where they could not use such mechanical versions because of intractable expectations and used instead simulations from their physical model, literally reinventing ABC. This resolution had the same feeling, closer to indirect inference than regular inference, although it took me half the defence to realise it.

The defence actually took part in the beautiful historical Perrault’s building of Observatoire de Paris, in downtown Paris, where Cassini, Arago and Le Verrier once ruled!  In the council room under paintings of major French astronomers, including Laplace himself, looking quite smug in his academician costume. The building is built around the Paris Zero Meridian (which got dethroned in 1911 by the Greenwich Zero Meridian, which I contemplated as a kid since my childhood church had the Greenwich drawn on the nave stones). The customary “pot” after the thesis and its validation by the jury was in the less historical cafeteria of the Observatoire, but it included a jazz big band, which made this thesis defence quite unique in many ways!